Results 271 to 280 of about 25,534 (310)
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CONGRUENCES CONCERNING LUCAS SEQUENCES
International Journal of Number Theory, 2014Let p be a prime greater than 3. In this paper, by using expansions and congruences for Lucas sequences and the theory of cubic residues and cubic congruences, we establish some congruences for [Formula: see text] and [Formula: see text] modulo p, where [x] is the greatest integer not exceeding x, and m is a rational p-adic integer with m ≢ 0 ( mod p).
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AIP Conference Proceedings, 2014
For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation Ln+1 = kLn+Ln−1 with the initial values L0 = 2, L1 = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.
C. K. Ho, Jye-Ying Sia, Chin-Yoon Chong
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For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation Ln+1 = kLn+Ln−1 with the initial values L0 = 2, L1 = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.
C. K. Ho, Jye-Ying Sia, Chin-Yoon Chong
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Tribonacci-Lucas Sequence Spaces
2022In this work, we basically define new sequence spaces using Tribonacci-Lucas numbers. Then, we give some inclusion relations by examining some topological properties of these spaces. We also characterize some matrix classes by calculating the Köthe-Toeplitz duals of our space.
KARAKAŞ, Murat, ŞEVİK, Uğurcan
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Primefree shifted Lucas sequences
Acta Arithmetica, 2015Summary: We say a sequence \(\mathcal S=(s_n)_{n\geq 0}\) is primefree if \(|s_n|\) is not prime for all \(n\geq 0\), and to rule out trivial situations, we require that no single prime divides all terms of \(\mathcal S\). In this article, we focus on the particular Lucas sequences of the first kind, \(\mathcal U_a=(u_n)_{n\geq 0}\), defined by \[ u_0 ...
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ON GENERALIZED LUCAS AND PELL-LUCAS SEQUENCES
2019In this paper, we define the generaziled Lucas sequences and the Pell-Lucas sequences. Further we give Binet-like formulas, generating function, sums formulas and some important identities which involving the generalized Lucas and Pell-Lucas Numbers.
Tas, Zisan Kusaksiz, TAŞCI, DURSUN
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Shifting Lucas Sequences Away from Primes
Summary: We strengthen a result of Jones by showing that for any positive integer \(P\), the Lucas sequence \((U_n)_n\) defined by \(U_0 = 0\), \(U_1 = 1\), \(U_n=P \cdot U_{n -1} + U_{n - 2}\) can be translated by a positive integer \(K(P)\) such that the shifted sequence with general term \(U_n + K(P)\) contains no primes, nor terms one unit away ...Ismailescu, Dan +4 more
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Mersenne Numbers in Generalized Lucas Sequences
Proceedings of the Bulgarian Academy of SciencesLet $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer.
Altassan, Alaa, ALAN, Murat
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Two generalizations of Lucas sequence
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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